First, similarly to eq. exposure, to bypass the nonsmoothness of the Gini index, [1]} optimize a surrogate with std, named eq. utility:
\(F^{\rm eq}(P) = \sum _{i=1}^n u_i(P) - \frac{\lambda }{n}\sqrt{\sum _{i=1}^n\left(u_i(P) - \frac{1}{n} \sum _{i^{\prime }=1}^n u_{i^{\prime }}(P)\right)^2}.\) 
